By Alessandro Astolfi, Lorenzo Marconi
This ebook is a tribute to Prof. Alberto Isidori at the party of his sixty fifth birthday. Prof. Isidori’s proli?c, pioneering and high-impact study task has spanned over 35 years. all through his profession, Prof. Isidori has constructed ground-breaking effects, has initiated researchdirections and has contributed towardsthe foundationofnonlinear controltheory.In addition,his commitment to provide an explanation for tricky matters and di?cult thoughts in an easy and rigorous means and to encourage younger researchers has been instrumental to the highbrow progress of the nonlinear keep an eye on group around the world. the quantity collects 27 contributions written through a complete of fifty two researchers. The central writer of every contribution has been chosen one of the - searchers who've labored with Prof. Isidori, have in?uenced his learn job, or have had the privilege and honour of being his PhD scholars. The contributions tackle a signi?cant variety of keep an eye on issues, together with th- retical matters, complicated functions, rising keep watch over instructions and educational works. the range of the components coated, the variety of participants and their overseas status supply proof of the impression of Prof. Isidori within the regulate and structures conception groups. The ebook has been divided into six elements: procedure research, Optimization tools, suggestions layout, law, Geometric equipment and Asymptotic research, re?ecting vital regulate components that have been strongly in- enced and, often times, pioneered by way of Prof. Isidori.
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Extra resources for Analysis and design of nonlinear control systems : in honor of Alberto Isidori
W| = l if w = Xi1 Xi2 · · · Xil . Let Lm e,∞ denote the set of measurable, locally essentially bounded functions u : [0, ∞) → Rm . For each u ∈ Lm e,∞ and S0 ∈ R[[Θ]], consider the initial value problem m ˙ S(t) = X0 + Xi u i S(t), S(0) = S0 (3) i=1 seen as a diﬀerential equation over R[[Θ]]. A solution is an absolutely continuous curve, where derivative is understood coeﬃcient-wise. For any locally essentially bounded u( · ), by the Peano-Baker formula, there is always a solution in R[[Θ]] whose coeﬃcients are iterated integrals of u.
Table 3. Examples of module speciﬁcations Type of module Specification Parameter resistor default R in Ohms n-terminal circuit transfer impedance G ∈ Rn×n (ξ) n-port circuit i/s/o admittance (A, B, C, D) bar, 2 applicators Lagrangian equations mass and length 2-inlet vessel default geometry signal processor kernel representation R ∈ IR[ξ]•×• signal processor latent variable (R, M ) etc. etc. etc. A module Σ of a given type with T terminals yields the signal space W = W1 × W2 × · · · × WT , with Wk the universum associated with the k-th terminal.
This is faithful to the physics, and should be contrasted with the graph structure pursued in electrical circuit theory, which has the modules in the branches and the connectors in the nodes. This works ﬁne with 2-terminal elements, but is awkward otherwise, and is diﬃcult to generalize to other, non-electrical, domains. 5 Interconnected Behavior We now formalize the interconnected system. The most eﬀective way to proceed is to specify it as a latent variable system, with as manifest variables the variables speciﬁed in the manifest variable assignment, and as latent variables all the terminal variables associated with all the modules.